Theoretical and Experimental Investigations of Coolant Flow in Inlet Channels of the BTA and Ejector Drills

1995 ◽  
Vol 209 (3) ◽  
pp. 211-220 ◽  
Author(s):  
V P Astakhov ◽  
P S Subramanya ◽  
M O M Osman
Keyword(s):  
Axial Flow ◽  
Annular Channel ◽  
Reynolds Numbers ◽  
Coolant Flow ◽  
Experimental Investigations ◽  
Annular Channels ◽  
Critical Reynolds Numbers ◽  
Flow Through ◽  
The Stability ◽  
The Mathematical Model

The coolant flow through inlet annular channels in BTA and ejector drills is investigated. The study was conducted in order to understand the influence of the channel's parameters (the channel's clearance variation along its length and eccentricity) on the coolant pressure distribution and hydraulic resistance. A new design of the ejector drill with the eccentrical location on the inner tube is proposed. A study is made of the stability in the coolant flow in the inlet annular channels. The appearance of instability is explained by the presence of Taylor macrovortices in these channels under certain combinations of boring bar rotating velocity and axial flow velocity. In order to define the unstable regimes (the critical Reynolds numbers), the mathematical model for non-isothermal flow through the annular channel is solved. The heat transfer from the swarf to the incoming coolant is investigated under different flow conditions.

scholarly journals Linear stability of boundary layers under solitary waves

2014 ◽  
Vol 761 ◽  
pp. 62-104 ◽  
Author(s):  
Joris C. G. Verschaeve ◽  
Geir K. Pedersen
Keyword(s):  
Linear Stability ◽  
Solitary Waves ◽  
Reynolds Numbers ◽  
Quantitative Agreement ◽  
Linear Instability ◽  
Navier Stokes ◽  
Acceleration Region ◽  
Critical Reynolds Numbers ◽  
Tollmien Schlichting ◽  
The Stability

AbstractIn the present treatise, the stability of the boundary layer under solitary waves is analysed by means of the parabolized stability equation. We investigate both surface solitary waves and internal solitary waves. The main result is that the stability of the flow is not of parametric nature as has been assumed in the literature so far. Not only does linear stability analysis highlight this misunderstanding, it also gives an explanation why Sumer et al. (J. Fluid Mech., vol. 646, 2010, pp. 207–231), Vittori & Blondeaux (Coastal Engng, vol. 58, 2011, pp. 206–213) and Ozdemir et al. (J. Fluid Mech., vol. 731, 2013, pp. 545–578) each obtained different critical Reynolds numbers in their experiments and simulations. We find that linear instability is possible in the acceleration region of the flow, leading to the question of how this relates to the observation of transition in the acceleration region in the experiments by Sumer et al. or to the conjecture of a nonlinear instability mechanism in this region by Ozdemir et al. The key concept for assessment of instabilities is the integrated amplification which has not been employed for this kind of flow before. In addition, the present analysis is not based on a uniformization of the flow but instead uses a fully nonlinear description including non-parallel effects, weakly or fully. This allows for an analysis of the sensitivity with respect to these effects. Thanks to this thorough analysis, quantitative agreement between model results and direct numerical simulation has been obtained for the problem in question. The use of a high-order accurate Navier–Stokes solver is primordial in order to obtain agreement for the accumulated amplifications of the Tollmien–Schlichting waves as revealed in this analysis. An elaborate discussion on the effects of amplitudes and water depths on the stability of the flow is presented.

The stability of a stratified fluid

1967 ◽  
Vol 29 (2) ◽  
pp. 233-240
Author(s):  
J. B. Hinwood
Keyword(s):  
Turbulent Flow ◽  
Froude Number ◽  
Reynolds Numbers ◽  
Stratified Fluid ◽  
Stratified Flows ◽  
Rectangular Duct ◽  
Interfacial Waves ◽  
Homogeneous Flow ◽  
Critical Reynolds Numbers ◽  
The Stability

For the flow of a stably-stratified fluid in the inlet region of a rectangular duct, it is shown experimentally that the upper and lower critical Reynolds numbers are functions of the interfacial Froude number F, and that if F is large they are lower than for a homogeneous flow. In stratified flows the disturbances leading to turbulent flow sometimes arise at the interface and lead to interfacial waves, whose wavelength at breaking is equal to the conduit depth.

An Experimental Investigation of the Stability of Spiral Vortex Flow

1979 ◽  
Vol 21 (6) ◽  
pp. 397-402 ◽  
Author(s):  
M. M. Sorour ◽  
J. E. R. Coney
Keyword(s):  
Vortex Flow ◽  
Outer Cylinder ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Vortex Cell ◽  
Annular Gap ◽  
Spiral Vortex ◽  
Axial Pressure Gradient ◽  
The Stability

The hydrodynamic stability of the flow in an annular gap, formed by a stationary outer cylinder and a rotatable inner cylinder, through which an axial flow of air can be imposed, is studied experimentally. Two annulus radius ratios of 0.8 and 0.955 are considered, representing wide- and narrow-gap conditions, respectively. It is shown that, when a large, axial pressure gradient is superimposed on the tangential flow induced by the rotation of the inner cylinder, the characteristics of the flow at criticality change significantly from those at zero and low axial flows, the axial length and width of the resultant spiral vortex departing greatly from the known dimensions of a Taylor vortex cell at zero axial flow. Also, the drift velocity of the spiral vortex is found to vary with the axial flow. Axial Reynolds numbers, Rea, of up to 700 are considered.

The Stability of Water Flow Over Heated and Cooled Flat Plates

1968 ◽  
Vol 90 (1) ◽  
pp. 109-114 ◽  
Author(s):  
Ahmed R. Wazzan ◽  
T. Okamura ◽  
A. M. O. Smith
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Stream Temperature ◽  
Heated Wall ◽  
Flat Plates ◽  
Critical Reynolds Numbers ◽  
The Stability ◽  
Sommerfeld Equation

The theory of two-dimensional instability of laminar flow of water over solid surfaces is extended to include the effects of heat transfer. The equation that governs the stability of these flows to Tollmien-Schlichting disturbances is the Orr-Sommerfeld equation “modified” to include the effect of viscosity variation with temperature. Numerical solutions to this equation at high Reynolds numbers are obtained using a new method of integration. The method makes use of the Gram-Schmidt orthogonalization technique to obtain linearly independent solutions upon numerically integrating the “modified Orr-Sommerfeld” equation using single precision arithmetic. The method leads to satisfactory answers for Reynolds numbers as high as Rδ* = 100,000. The analysis is applied to the case of flow over both heated and cooled flat plates. The results indicate that heating and cooling of the wall have a large influence on the stability of boundary-layer flow in water. At a free-stream temperature of 60 deg F and wall temperatures of 60, 90, 120, 135, 150, 200, and 300deg F, the critical Reynolds numbers Rδ* are 520, 7200, 15200, 15600, 14800, 10250, and 4600, respectively. At a free-stream temperature of 200F and wall temperature of 60 deg F (cooled case), the critical Reynolds number is 151. Therefore, it is evident that a heated wall has a stabilizing effect, whereas a cooled wall has a destabilizing effect. These stability calculations show that heating increases the critical Reynolds number to a maximum value (Rδ* max = 15,700 at a temperature of TW = 130 deg F) but that further heating decreases the critical Reynolds number. In order to determine the influence of the viscosity derivatives upon the results, the critical Reynolds number for the heated case of T∞ = 40 and TW = 130 deg F was determined using (a) the Orr-Sommerfeld equation and (b) the present governing equation. The resulting critical Reynolds numbers are Rδ* = 140,000 and 16,200, respectively. Therefore, it is concluded that the terms pertaining to the first and second derivatives of the viscosity have a considerable destabilizing influence.

Global Linear Instability of Flow Through a Converging–Diverging Channel

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
Mamta R. Jotkar ◽  
Gayathri Swaminathan ◽  
Kirti Chandra Sahu ◽  
Rama Govindarajan
Keyword(s):  
Reynolds Numbers ◽  
Linear Instability ◽  
Stability Study ◽  
Base Flow ◽  
Low Reynolds Numbers ◽  
Critical Reynolds Numbers ◽  
Diverging Channel ◽  
Order Of Magnitude ◽  
Flow Through ◽  
Low Reynolds

The global linear stability, where we assume no homogeneity in either of the spatial directions, of a two-dimensional laminar base flow through a spatially periodic converging–diverging channel is studied at low Reynolds numbers. A large wall-waviness amplitude is used to achieve instability at critical Reynolds numbers below ten. This is in contrast to earlier studies, which were at lower wall-waviness amplitude and had critical Reynolds numbers an order of magnitude higher. Moreover, our leading mode is a symmetry-breaking standing mode, unlike the traveling modes which are standard at higher Reynolds numbers. Eigenvalues in the spectrum lie on distinct branches, showing varied structure spanning the geometry. Our global stability study suggests that such modes can be tailored to give enhanced mixing in microchannels at low Reynolds numbers.

Hydrodynamic instability of viscous flow between rotating coaxial cylinders with fully developed axial flow

1977 ◽  
Vol 81 (4) ◽  
pp. 641-655 ◽  
Author(s):  
K. C. Chung ◽  
K. N. Astill
Keyword(s):  
Amplification Factor ◽  
Hydrodynamic Instability ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Spiral Flow ◽  
Small Perturbations ◽  
Coaxial Cylinders ◽  
Counter Rotation ◽  
Concentric Cylinders ◽  
The Stability

A linear stability analysis is presented for flow between concentric cylinders when a fully developed axial flow is present. Small perturbations are assumed to be nonaxisymmetric. This leads to an eigenvalue problem with four eigenvalues: the critical Taylor number, an amplification factor and two wavenumbers. The presence of the tangential wavenumber permits prediction of the stability of spiral flow. This made it possible to model the flow more accurately and to extend the range of calculations to higher axial Reynolds numbers than had previously been attainable. Calculations were carried out for radius ratios from 0·95 to 0·1, Reynolds numbers as large as 300 and cases with co-rotation and counter-rotation of the cylinders.

Influence of circumferential annular grooving design of impeller on suspended fluid force of axial flow blood pump

2022 ◽  
pp. 039139882110649
Author(s):  
Liang Wang ◽  
Zhong Yun ◽  
Xiaoyan Tang ◽  
Chuang Xiang
Keyword(s):  
Axial Flow ◽  
Groove Depth ◽  
Blood Pump ◽  
Suspension Stability ◽  
Impeller Blade ◽  
Stable Suspension ◽  
Axial Flow Blood Pump ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

Aiming at insufficient suspension force on the impeller when the hydraulic suspension axial flow blood pump is start at low speed, the impeller suspension stability is poor, and can’t quickly enter the suspended working state. By establishing the mathematical model of the suspension force on the impeller, then the influence of the circumferential groove depth of the impeller on the suspension force is analyzed, and the annular groove depth on the impeller blade in the direction of fluid inlet and outlet was determined as (0.26, 0.02 mm). When the blood pump starts, there is an eccentricity between the impeller and the pump tube, the relationship between the suspension force and the speed of the impeller under different eccentricities is analyzed. Combined with the prototype experiment, the circumferential annular grooving design of the impeller can make the blood pump rotate at about 3500 rpm into the suspension state, when the impeller is at 8000 rpm, the impeller can basically achieve stable suspension at the eccentricity of 0.1 mm in the gravity direction, indicating that the reasonable circumferential annular grooving design of the impeller can effectively improve the suspension hydraulic force of the impeller and improve the stability of the hydraulic suspension axial flow blood pump.

On the stability of flow in an elliptic pipe which is nearly circular

1978 ◽  
Vol 87 (2) ◽  
pp. 233-241 ◽  
Author(s):  
A. Davey
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Cross Section ◽  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Major Axis ◽  
Reynolds Numbers ◽  
Minor Axis ◽  
Critical Reynolds Numbers ◽  
The Stability

The linear stability of Poiseuille flow in an elliptic pipe which is nearly circular is examined by regarding the flow as a perturbation of Poiseuille flow in a circular pipe. We show that the temporal damping rates of non-axisymmetric infinitesimal disturbances which are concentrated near the wall of the pipe are decreased by the ellipticity. In particular we estimate that if the length of the minor axis of the cross-section of the pipe is less than about 96 ½% of that of the major axis then the flow will be unstable and a critical Reynolds number will exist. Also we calculate estimates of the ellipticities which will produce critical Reynolds numbers ranging from 1000 upwards.

scholarly journals Fluid friction between rotating cylinders I—Torque measurements

1936 ◽  
Vol 157 (892) ◽  
pp. 546-564 ◽  
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Centrifugal Force ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Stream Line ◽  
Rotating Cylinders ◽  
Torque Measurements ◽  
Critical Reynolds Numbers ◽  
The Stability

The stability of fluid contained between concentric rotating cylinders has been investigated and it has been shown that, when only the inner cylinder rotates, the flow becomes unstable when a certain Reynolds number of the flow is exceeded. When the outer cylinder only is rotated, the flow is stable so far as disturbances of the type produced in the former case are concerned, but provided the Reynolds number of the flow exceeds a certain value, turbulence sets in. The object of the present experiments was partly to measure the torque reaction between two cylinders in the two cases in order to find the effect of centrifugal force on the turbulence, and partly to find the critical Reynolds numbers for the transition from stream-line to turbulent flow. The apparatus is shown diagrammatically in fig. 1.

Experimental Investigations of Couette-Taylor-Poiseuille Flows Using the Electro-Diffusional Technique

2016 ◽  
Author(s):  
Emna Berrich ◽  
Fethi Aloui ◽  
Jack Legrand
Keyword(s):  
Mass Transfer ◽  
Shear Rate ◽  
Mass Transfer Rate ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Wall Shear Rate ◽  
Experimental Investigations ◽  
Local Mass ◽  
Local Mass Transfer ◽  
Wall Shear

Couette-Taylor-Poiseuille flow CTPF consists on the superposition of Couette-Taylor flow to an axial flow. The CTPF flow hydrodynamics studies remain rather qualitative or numerical or are restricted to relatively low Taylor and/or axial Reynolds numbers. For more comprehensive and control of CTPF, especially for relatively high Taylor numbers and high axial Reynolds numbers, we investigated experimentally CTF with and without an axial flow, using the electro-diffusion ED method. This technique requires the use of Electro-Diffusion ED probe which allows the determination of the local mass transfer rate from the Limiting Diffusion current measurement delivered by the ED probe while it is polarized by a polarization voltage. From the local mass transfer (the Sherwood number), we determined the wall shear rate using different approaches. The results illustrate that low axial flow can generate a stabilizing effect on the CT flow. The time-evolutions of the local mass transfer and the wall shear rate are periodic. These evolutions characterize the waviness or the stretching of the vortices. However, Taylor Wavy Vortex Flow TWVF is destabilized under the effect of relatively important axial flow. The time-evolutions of wall shear rate are no longer periodic. Indeed, Taylor vortices are overlapped or completely destructed.

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